[libc-commits] [libc] [libc][math][c23] Add exp2m1f C23 math function (PR #86996)
via libc-commits
libc-commits at lists.llvm.org
Tue Apr 2 07:00:55 PDT 2024
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@@ -0,0 +1,182 @@
+//===-- Implementation of exp2m1f function --------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/exp2m1f.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/macros/properties/cpu_features.h"
+#include "src/errno/libc_errno.h"
+
+#include "explogxf.h"
+
+namespace LIBC_NAMESPACE {
+
+static constexpr size_t N_EXCEPTS_LO = 8;
+
+static constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP2M1F_EXCEPTS_LO =
+ {{
+ // (input, RZ output, RU offset, RD offset, RN offset)
+ // x = 0x1.36dc8ep-36, exp2m1f(x) = 0x1.aef212p-37 (RZ)
+ {0x2d9b'6e47U, 0x2d57'7909U, 1U, 0U, 0U},
+ // x = 0x1.224936p-19, exp2m1f(x) = 0x1.926c0ep-20 (RZ)
+ {0x3611'249bU, 0x35c9'3607U, 1U, 0U, 1U},
+ // x = 0x1.d16d2p-20, exp2m1f(x) = 0x1.429becp-20 (RZ)
+ {0x35e8'b690U, 0x35a1'4df6U, 1U, 0U, 1U},
+ // x = 0x1.17949ep-14, exp2m1f(x) = 0x1.8397p-15 (RZ)
+ {0x388b'ca4fU, 0x3841'cb80U, 1U, 0U, 1U},
+ // x = -0x1.9c3e1ep-38, exp2m1f(x) = -0x1.1dbeacp-38 (RZ)
+ {0xacce'1f0fU, 0xac8e'df56U, 0U, 1U, 0U},
+ // x = -0x1.4d89b4p-32, exp2m1f(x) = -0x1.ce61b6p-33 (RZ)
+ {0xafa6'c4daU, 0xaf67'30dbU, 0U, 1U, 1U},
+ // x = -0x1.a6eac4p-10, exp2m1f(x) = -0x1.24fadap-10 (RZ)
+ {0xbad3'7562U, 0xba92'7d6dU, 0U, 1U, 1U},
+ // x = -0x1.e7526ep-6, exp2m1f(x) = -0x1.4e53dep-6 (RZ)
+ {0xbcf3'a937U, 0xbca7'29efU, 0U, 1U, 1U},
+ }};
+
+static constexpr size_t N_EXCEPTS_HI = 2;
+
+static constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP2M1F_EXCEPTS_HI =
+ {{
+ // (input, RZ output, RU offset, RD offset, RN offset)
+ // x = 0x1.16a972p-1, exp2m1f(x) = 0x1.d545b2p-2 (RZ)
+ {0x3f0b'54b9U, 0x3eea'a2d9U, 1U, 0U, 0U},
+ // x = -0x1.9f12acp-5, exp2m1f(x) = -0x1.1ab68cp-5 (RZ)
+ {0xbd4f'8956U, 0xbd0d'5b46U, 0U, 1U, 0U},
+ }};
+
+LLVM_LIBC_FUNCTION(float, exp2m1f, (float x)) {
+ using FPBits = fputil::FPBits<float>;
+ FPBits xbits(x);
+
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & 0x7fff'ffffU;
+
+ // When |x| >= 128, or x is nan, or |x| <= 2^-5
+ if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {
+ // |x| <= 2^-5
+ if (x_abs <= 0x3d00'0000) {
+ if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+
+ // Minimax polynomial generated by Sollya with:
+ // > display = hexadecimal;
+ // > fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);
+ constexpr double COEFFS[] = {
+ 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,
+ 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};
+ double xd = x;
+ double xsq = xd * xd;
+ double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);
+ double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);
+ double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);
+ double p = fputil::polyeval(xsq, c0, c1, c2);
+ return static_cast<float>(p * xd);
+ }
+
+ // x >= 128, or x is nan
+ if (xbits.is_pos()) {
+ if (xbits.is_finite()) {
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return FPBits::max_normal().get_val();
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_OVERFLOW);
+ }
+
+ // x >= 128 and 2^x - 1 rounds to +inf, or x is +inf or nan
+ return x + FPBits::inf().get_val();
+ }
+ }
+
+ if (LIBC_UNLIKELY(x <= -25.0f)) {
+ // 2^(-inf) - 1 = -1
+ if (xbits.is_inf())
+ return -1.0f;
+ // 2^nan - 1 = nan
+ if (xbits.is_nan())
+ return x;
+
+ int rounding = fputil::quick_get_round();
+ if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO)
+ return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
+
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return -1.0f;
+ }
+
+ if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+ return r.value();
+
+ // For -25 < x < 128, to compute 2^x, we perform the following range
+ // reduction: find hi, mid, lo such that:
+ // x = hi + mid + lo, in which:
+ // hi is an integer,
+ // 0 <= mid * 2^5 < 32 is an integer,
+ // -2^(-6) <= lo <= 2^(-6).
+ // In particular,
+ // hi + mid = round(x * 2^5) * 2^(-5).
+ // Then,
+ // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.
+ // 2^mid is stored in the lookup table of 32 elements.
+ // 2^lo is computed using a degree-4 minimax polynomial generated by Sollya.
+ // We perform 2^hi * 2^mid by simply add hi to the exponent field of 2^mid.
+
+ // kf = (hi + mid) * 2^5 = round(x * 2^5)
+ float kf;
+ int k;
+#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
+ kf = fputil::nearest_integer(x * 32.0f);
+ k = static_cast<int>(kf);
+#else
+ constexpr float HALF[2] = {0.5f, -0.5f};
+ k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));
+ kf = static_cast<float>(k);
+#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
+
+ // dx = lo = x - (hi + mid) = x - kf * 2^(-5)
+ double dx = fputil::multiply_add(-0x1.0p-5f, kf, x);
+
+ // hi = floor(kf * 2^(-4))
+ // exp_hi = shift hi to the exponent field of double precision.
+ int64_t exp_hi =
+ static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)
+ << fputil::FPBits<double>::FRACTION_LEN);
+ // mh = 2^hi * 2^mid
+ // mh_bits = bit field of mh
+ int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;
+ double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val();
+
+ // Degree-4 polynomial approximating (2^x - 1)/x generated by Sollya with:
+ // > display = hexadecimal;
+ // > fpminimax((2^x - 1)/x, 4, [|D...|], [-2^-6, 2^-6]);
+ constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,
+ 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,
+ 0x1.5d88091198529p-10};
+ double dx_sq = dx * dx;
+ double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0);
+ double c2 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);
+ double c3 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);
+ double p = fputil::multiply_add(dx_sq, c3, c2);
+ // 2^x = 2^(hi + mid + lo)
+ // = 2^(hi + mid) * 2^lo
+ // ~ mh * (1 + lo * P(lo))
+ // = mh + (mh*lo) * P(lo)
+ double exp2_lo = fputil::multiply_add(p, dx_sq, c1);
----------------
lntue wrote:
You can combine these into `double p = fputil::polyeval(dx_sq, c1, c2, c3);`
Also update the comment to reflect the computation steps are done here: `mh * exp2_lo - 1`.
https://github.com/llvm/llvm-project/pull/86996
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